Abstract
This paper studies the fully distributed tracking problem for high-order nonlinear multi-agent systems (MASs) with directed graph. Unlike global Lipschitz condition, the nonlinear function we considered only needs to be a continuously differential one. A recursive state transformation and adaptive control technique are employed to design the tracking controllers. First, a discontinuous fully distributed tracking controller is developed for MASs. Under this controller, the follower agents track the leader agent asymptotically. Second, a continuous fully distributed tracking controller is purposely presented for MASs to avoid the chattering problem may caused by discontinuous controller. Finally, a numerical example is given to verify the effectiveness of those two fully distributed controllers.
Highlights
Past two decades witnessed the rapid development of distributed control of multiagent systems (MASs) for its practical applications in engineering
A nonlinear function satisfies neural network approximation assumption means that it can be approximated by the product of a known basis function and an unknown neural network weight matrix
By using Lyapunov design method, Wang firstly proposed a new kind of adaptive control method for fully distributed tracking problem of first-order nonlinear leader-follower MASs with directed graph in [8], and extended this control method to second-order nonlinear
Summary
Past two decades witnessed the rapid development of distributed control of MASs for its practical applications in engineering. Distributed control, which does not use any global topology information, has attracted many researchers’ attention Yu and his coauthors firstly studied fully distributed cooperative control problems for second-order nonlinear MASs with undirected graph via agent-based adaptive gains [4]. By using Lyapunov design method, Wang firstly proposed a new kind of adaptive control method for fully distributed tracking problem of first-order nonlinear leader-follower MASs with directed graph in [8], and extended this control method to second-order nonlinear. Unlike global Lipschitz assumption, neural network approximation assumption and manifold assumption, the nonlinear function in this paper only needs to be a continuously differential function Wang and his coauthors had studied fully distributed tracking problems for first-order and second-order nonlinear MASs with such kind of nonlinearity in [8], [9]. Assumption 2: The input uN+1 of leader agent is bounded by a known constant τ ≥ 0, i.e., |uN+1| ≤ τ
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